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Long-standing problem: The nuclear level density angular-momentum dependence and isomeric data assessment

M. Avrigeanu1,*, E. Šimečková2,†, J. Mrázek2, X. Ledoux3, J. Novak2, M. Štefánik2, M. Ansorge2, A. Cassisa2, J. Kozic2 et al.

C. Costache1 and V. Avrigeanu1

  • *Contact author: marilena.avrigeanu@nipne.ro
  • †Contact author: simeckova@ujf.cas.cz
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Phys. Rev. Research 8, 023001 – Published 1 April, 2026

DOI: https://doi.org/10.1103/cjqq-6psq

Abstract

Recent Tc91,92,93 activation for deuterons incident on Monat has become a challenge for the nuclear level density (NLD) angular-momentum dependence. Actually, replacement of the moment of inertia rigid-body value Ir by half of it, within a given NLD parameter set, demands a change of the rest of NLD parameters significantly beyond their fitted limits. The corresponding uncertainty of calculated cross sections versus the NLD parameter accuracy is also higher, while use of either the same or distinct compound-nucleus and preequilibrium emission spin distributions becomes significant at higher incident energies. Nevertheless, the current way to describe experimental isomeric cross sections by using at most half of Ir values provides agreement of the measured and calculated data at the price of less and less correct NLDs. The moment of inertia relevance for the NLD correctness also emphasizes the value of a direct method to endorse it. Further measurements of average resonance spacings of s-wave neutrons and protons, corresponding to different spins of the same nucleus, are therefore highly demanded.

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References (78)

  1. E. Šimečková, M. Avrigeanu, J. Mrázek, X. Ledoux, J. Novak, M. Štefánik, M. Ansorge, A. Cassisa, J. Kozic, C. Costache, et al., Deuteron-induced neutron emission on molybdenum at low energies, Phys. Rev. C 111, 044612 (2025).
  2. E. Šimečková, M. Avrigeanu, J. Mrázek, X. Ledoux, J. Novak, M. Štefánik, M. Ansorge, A. Cassisa, J. Kozic, C. Costache, et al., Deuteron-induced charged-particle emission on molybdenum at low energies, Phys. Rev. C (to be published).
  3. W. Hauser and H. Feshbach, The inelastic scattering of neutrons, Phys. Rev. 87, 366 (1952).
  4. E. Gadioli and P. E. Hodgson, Pre-equilibrium Nuclear Reactions (Clarendon, Oxford, 1992).
  5. H. A. Bethe, Nuclear physics B. Nuclear dynamics, theoretical, Rev. Mod. Phys. 9, 69 (1937).
  6. C. Bloch, Theory of nuclear level density, Phys. Rev. 93, 1094 (1954).
  7. T. Ericson, A statistical analysis of excited nuclear states, Nucl. Phys. 11, 481 (1959).
  8. M. Avrigeanu, V. Avrigeanu, M. Diakaki, and R. Vlastou, Isomeric cross sections of fast-neutron-induced reactions on Au197, Phys. Rev. C 85, 044618 (2012).
  9. A. Rodrigo, N. Otuka, S. Takács, and A. Koning, Compilation of isomeric ratios of light particle induced nuclear reactions, At. Data Nucl. Data Tables 153, 101583 (2023).
  10. M. B. Chadwick, P. G. Young, P. Oblozinsky, and A. Marcinkowski, Preequilibrium spin effects in Feshbach-Kerman-Koonin and exciton models and application to high-spin isomer production, Phys. Rev. C 49, R2885(R) (1994).
  11. T. Kawano, P. Talou, and M. B. Chadwick, Production of isomers by neutron-induced inelastic scattering on Ir193 and influence of spin distribution in the pre-equilibrium process, Nucl. Instrum. Methods Phys. Res., Sect. A 562, 774 (2006).
  12. D. Dashdorj, T. Kawano, P. E. Garrett, J. A. Becker, U. Agvaanluvsan, L. A. Bernstein, M. B. Chadwick, M. Devlin, N. Fotiades, G. E. Mitchell, R. O. Nelson, W. Younes, Effect of preequilibrium spin distribution on Ti48+ n cross sections, Phys. Rev. C 75, 054612 (2007).
  13. N. Fotiades, R. O. Nelson, M. Devlin, S. Holloway, T. Kawano, P. Talou, M. B. Chadwick, J. A. Becker, and P. E. Garrett, Feeding of the 11/2− isomers in stable Ir and Au isotopes, Phys. Rev. C 80, 044612 (2009).
  14. H. Feshbach, A. Kerman, and S. Koonin, The statistical theory of multi-step compound and direct reactions, Ann. Phys. 125, 429 (1980).
  15. H. Gruppelaar, Level density in unified pre-equilibrium and equilibrium models, in IAEA Advisory Group Meeting on Basic and Applied Problems of Nuclear Level Densities, Upton, New York, April 11–15, 1983, edited by M. R. Bhat (Brookhaven National Laboratory, 1983), Upton, Report BNL-NCS-51694, p. 143.
  16. C. Y. Fu, Simplified spin cutoff factors for particle-hole level densities in precompound nuclear reaction theory, Nucl. Sci. Eng. 92, 440 (1986).
  17. A. Koning, S. Hilaire, and S. Goriely, TALYS: Modeling of nuclear reactions, Eur. Phys. J. A 59, 131 (2023).
  18. M. B. Fox, A. S. Voyles, J. T. Morrell, L. A. Bernstein, A. M. Lewis, A. J. Koning, J. C. Batchelder, E. R. Birnbaum, C. S. Cutler, D. G. Medvedev, et al., Investigating high-energy proton-induced reactions on spherical nuclei: Implications for the preequilibrium exciton model, Phys. Rev. C 103, 034601 (2021).
  19. M. Avrigeanu, E. Šimečková, J. Mrázek, X. Ledoux, J. Novak, M. Štefánik, M. Ansorge, A. Cassisa, J. Kozic, C. Costache, et al., Technical Report, EUROfusion Consortium Report EUROFUSION WPBB-PR(26) 41144, Garching, Germany, 2026, https://pinboard.euro-fusion.org/repository/submitted/WPBBPR26_41144_submitted.pdf.
  20. W. Dilg, W. Schantl, H. Vonach, and M. Uhl, Level density parameters for the back-shifted Fermi gas model in the mass range 40 < A < 250, Nucl. Phys. A 217, 269 (1973).
  21. H. Vonach, M. Uhl, B. Strohmaier, B. W. Smith, E. G. Bilpuch, and G. E. Mitchell, Comparison of average s-wave resonance spacings from proton and neutron resonances, Phys. Rev. C 38, 2541 (1988).
  22. H. Weigmann, C. Wagemans, A. Emsallem, and M. Asghar, Study of neutron induced charged particle reactions on K40: II. Resonance neutrons, Nucl. Phys. A 368, 117 (1981).
  23. V. Avrigeanu, T. Glodariu, A. J. M. Plompen, and H. Weigmann, On consistent description of nuclear level density, J. Nucl. Sci. Technol. 39, 746 (2002).
  24. D. J. Dean, S. E. Koonin, K. Langanke, P. B. Radha, and Y. Alhassid, Thermal properties of Fe54, Phys. Rev. Lett. 74, 2909 (1995).
  25. K. Langanke, D. Dean, S. Koonin, and P. Radha, Pairing correlations in N∼Z pf-shell nuclei, Nucl. Phys. A 613, 253 (1997).
  26. Y. Alhassid, G. F. Bertsch, L. Fang, and S. Liu, Nuclear moment of inertia and spin distribution of nuclear levels, Phys. Rev. C 72, 064326 (2005).
  27. Y. Alhassid, S. Liu, and H. Nakada, Spin projection in the shell model Monte Carlo method and the spin distribution of nuclear level densities, Phys. Rev. Lett. 99, 162504 (2007).
  28. M. Avrigeanu and V. Avrigeanu, Consistent optical potential for incident and emitted low-energy α particles. III. Nonstatistical processes induced by neutrons on Zr, Nb, and Mo nuclei, Phys. Rev. C 107, 034613 (2023).
  29. V. Semkova, V. Avrigeanu, T. Glodariu, A. Koning, A. Plompen, D. Smith, and S. Sudár, A systematic investigation of reaction cross sections and isomer ratios for neutrons up to 20 MeV on Ni-isotopes and 59Co by measurements with the activation technique and new model studies of the underlying reaction mechanisms, Nucl. Phys. A 730, 255 (2004).
  30. Evaluated nuclear structure data file (ENSDF), http://www.nndc.bnl.gov/ensdf/.
  31. R. Capote, M. Herman, P. Obložinský, P. G. Young, S. Goriely, T. Belgya, A. V. Ignatyuk, A. J. Koning, S. Hilaire, V. A. Plujko, et al., RIPL—Reference Input Parameter Library for calculation of nuclear reactions and nuclear data evaluations, Nucl. Data Sheets 110, 3107 (2009).
  32. H. Utsunomiya, S. Goriely, T. Kondo, C. Iwamoto, H. Akimune, T. Yamagata, H. Toyokawa, H. Harada, F. Kitatani, Y.-W. Lui, et al., Photoneutron cross sections for Mo isotopes: A step toward a unified understanding of (γ,n) and (n,γ) reactions, Phys. Rev. C 88, 015805 (2013).
  33. P. E. Koehler, Improved Mo95 neutron resonance parameters and astrophysical reaction rates, Phys. Rev. C 105, 054306 (2022).
  34. M. Guttormsen, A. C. Larsen, F. L. Bello Garrote, Y. Byun, T. K. Eriksen, F. Giacoppo, A. Görgen, T. W. Hagen, M. Klintefjord, H. T. Nyhus, et al., Shell-gap-reduced level densities in Y89,90, Phys. Rev. C 90, 044309 (2014).
  35. V. Avrigeanu and M. Avrigeanu, Validation of an optical potential for incident and emitted low-energy α-particles in the A∼60 mass range, Eur. Phys. J. A 57, 54 (2021).
  36. V. Avrigeanu and M. Avrigeanu, Validation of an optical potential for incident and emitted low-energy α-particles in the A∼60 mass range. II. Neutron-induced reactions on Ni isotopes, Eur. Phys. J. A 58, 189 (2022).
  37. M. Avrigeanu and V. Avrigeanu, Giant quadrupole resonances within neutron-induced α-particle emission? Phys. Lett. B 858, 139078 (2024).
  38. M. Avrigeanu, E. Šimečková, J. Mrázek, C. Costache, and V. Avrigeanu, Modeling of deuteron-induced reactions on molybdenum at low energies, J. Fusion Energy 43, 15 (2024).
  39. S. Kunieda, R. C. Haight, T. Kawano, M. B. Chadwick, S. M. Sterbenz, F. B. Bateman, O. A. Wasson, S. M. Grimes, P. Maier-Komor, H. Vonach, et al., Measurement and model analysis of (n,xα) cross sections for Cr, Fe, Co59, and Ni58,60 from threshold energy to 150 MeV, Phys. Rev. C 85, 054602 (2012).
  40. Average neutron resonance parameters and other data collected in Beijing, https://www-nds.iaea.org/ripl/resonances/other_files/beijing_dat.htm.
  41. A. Ignatyuk, G. Smirenkin, and A. Tishin, Phenomenological description of energy dependence of the level density parameter, Yad. Fiz. 21, 485 (1975).
  42. A. Junghans, M. de Jong, H.-G. Clerc, A. Ignatyuk, G. Kudyaev, and K.-H. Schmidt, Projectile-fragment yields as a probe for the collective enhancement in the nuclear level density, Nucl. Phys. A 629, 635 (1998).
  43. A. J. Koning and M. B. Chadwick, Microscopic two-component multistep direct theory for continuum nuclear reactions, Phys. Rev. C 56, 970 (1997).
  44. C. H. Johnson, Statistical model radiation widths for 75 < A < 130 and the enhancement of P-wave neutron capture for A≈90, Phys. Rev. C 16, 2238 (1977).
  45. P. Reimer, V. Avrigeanu, S. V. Chuvaev, A. A. Filatenkov, T. Glodariu, A. Koning, A. J. M. Plompen, S. M. Qaim, D. L. Smith, and H. Weigmann, Reaction mechanisms of fast neutrons on stable Mo isotopes below 21 MeV, Phys. Rev. C 71, 044617 (2005).
  46. M. Avrigeanu and V. Avrigeanu, Technical Report, Institute for Physics and Nuclear Engineering Reports NP-63-1987 and NP-86-1995, Bucharest, (1987/1995), www.oecd-nea.org/tools/abstract/detail/iaea0971/.
  47. M. Avrigeanu, M. Ivascu, and V. Avrigeanu, Pre-equilibrium emission in neutron induced reactions on Fe54,56, Z. Phys. A 329, 177 (1988).
  48. M. Avrigeanu, M. Ivascu, and V. Avrigeanu, Nuclear level densities below 40 MeV excitation energy in the mass region A≈50, Z. Phys. A 335, 299 (1990).
  49. M. Avrigeanu and V. Avrigeanu, Partial level densities for nuclear data calculations, Comput. Phys. Commun. 112, 191 (1998).
  50. M. Uhl and B. Strohmaier, Technical Report, Institut für Radiumforschung und Kernphysik Report IRK/01, Vienna, (1976).
  51. M. Uhl, Technical Report, IAEA-190, IAEA, Vienna, Austria, 1976, p. 361, https://nds.iaea.org/records/an431-dav76.
  52. H. Vonach, Technical Report, Lawrence Livermore National Laboratory Report UCID-19549, U.S. DOE Office of Scientific and Technical Information, Livermore, 1982, https://doi.org/10.2172/5029299.
  53. A. J. Koning and J. P. Delaroche, Local and global nucleon optical models from 1 keV to 200 MeV, Nucl. Phys. A 713, 231 (2003).
  54. V. Avrigeanu, M. Avrigeanu, and C. Mănăilescu, Further explorations of the α-particle optical model potential at low energies for the mass range A≈45−209, Phys. Rev. C 90, 044612 (2014).
  55. W. W. Daehnick, J. D. Childs, and Z. Vrcelj, Global optical model potential for elastic deuteron scattering from 12 to 90 MeV, Phys. Rev. C 21, 2253 (1980).
  56. V. V. Zerkin and B. Pritychenko, The experimental nuclear reaction data (EXFOR): Extended computer database and web retrieval system, Nucl. Instrum. Methods Phys. Res. Sect. A 888, 31 (2018).
  57. UiO/OCL level densities and gamma-ray strength functions, http://ocl.uio.no/compilation.
  58. M. Blann and H. K. Vonach, Global test of modified precompound decay models, Phys. Rev. C 28, 1475 (1983).
  59. M. Avrigeanu, A. Harangozo, V. Avrigeanu, and A. N. Antonov, Nuclear surface localization of preequilibrium reactions at low energies, Phys. Rev. C 54, 2538 (1996).
  60. M. Avrigeanu and V. Avrigeanu, Energy-dependent single-particle state density effects in the hybrid model of pre-equilibrium nuclear reactions, J. Phys. G: Nucl. Part. Phys. 20, 613 (1994).
  61. A. Harangozo, I. Şteţcu, M. Avrigeanu, and V. Avrigeanu, Particle-hole state densities with nonequidistant single-particle levels, Phys. Rev. C 58, 295 (1998).
  62. M. Herman, G. Reffo, M. Rosetti, G. Giardina, and A. Italiano, Eigenvalue spacings of the shell-model Hamiltonian, Phys. Rev. C 40, 2870 (1989).
  63. C. Kalbach, Surface effects in the exciton model of preequilibrium nuclear reactions, Phys. Rev. C 32, 1157 (1985).
  64. G. Reffo and M. Herman, Spin distribution of exciton levels for spherical nuclei, Lett. Nuovo Cimento 34, 261 (1982).
  65. P. D. Kunz, DWUCK4 User Manual (1984), http://spot.colorado.edu/~kunz/DWBA.html, http://www.oecd-nea.org/tools/abstract/detail/nesc9872/.
  66. S. Raman, C. W. Nestor, and P. Tikkanen, Transition probability from the ground to the first-excited 2+ state of even–even nuclides, At. Data Nucl. Data Tables 78, 1 (2001).
  67. T. Kibédi and R. H. Spear, Reduced electric-octupole transition probabilities, B(E3;01+→31−)—An update, At. Data Nucl. Data Tables 80, 35 (2002).
  68. I. J. Thompson, Coupled reaction channels calculations in nuclear physics, Comput. Phys. Rep. 7, 167 (1988)
  69. M. Avrigeanu, W. von Oertzen, R. A. Forrest, A. C. Obreja, F. L. Roman, and V. Avrigeanu, Analysis of deuteron elastic scattering and induced activation cross-sections of light and medium nuclei for IFMIF EVEDA, Fusion Eng. Des. 84, 418 (2009).
  70. M. Avrigeanu and V. Avrigeanu, Role of breakup and direct processes in deuteron-induced reactions at low energies, Phys. Rev. C 92, 021601(R) (2015).
  71. M. Avrigeanu and V. Avrigeanu, Additive empirical parametrization and microscopic study of deuteron breakup, Phys. Rev. C 95, 024607 (2017).
  72. M. Avrigeanu, D. Rochman, A. J. Koning, U. Fischer, D. Leichtle, C. Costache, and V. Avrigeanu, Advanced breakup-nucleon enhancement of deuteron-induced reaction cross sections, Eur. Phys. J. A 58, 3 (2022).
  73. M. G. Mustafa, T. Tamura, and T. Udagawa, Direct-reaction plus statistical-model analysis of the Cr52(d,2n)Mng,m52 reaction, Phys. Rev. C 35, 2077 (1987).
  74. A. J. Koning, D. Rochman, J.-C. Sublet, N. Dzysiuk, M. Fleming, and S. van der Marck, TENDL: Complete nuclear data library for innovative nuclear science and technology, Nucl. Data Sheets 155, 1 (2019).
  75. A. S. Voyles, L. A. Bernstein, E. R. Birnbaum, J. W. Engle, S. A. Graves, T. Kawano, A. M. Lewis, and F. M. Nortier, Excitation functions for (p, x) reactions of niobium in the energy range of Ep=40–90 MeV, Nucl. Instrum. Methods Phys. Res., Sect. B 429, 53 (2018).
  76. Z. Řanda and K. Svoboda, Excitation functions and yields of (d, n) and (d, 2n) reactions on natural molybdenum, J. Inorg. Nucl. Chem. 38, 2289 (1976).
  77. S. J. Freeman, D. K. Sharp, S. A. McAllister, B. P. Kay, C. M. Deibel, T. Faestermann, R. Hertenberger, A. J. Mitchell, J. P. Schiffer, S. V. Szwec, et al., Experimental study of the rearrangements of valence protons and neutrons amongst single-particle orbits during double-β decay in Mo100, Phys. Rev. C 96, 054325 (2017).
  78. W. Nörenberg, in Heavy Ion Collisions, edited by R. Bock (North-Holland, Amsterdam, 1980), Vol. 2, p. 1.

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Phys. Rev. Research 8, 023001– Published 1 April, 2026
  • Received 29 September 2025
  • Accepted 6 March 2026
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